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An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

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Journal of Ocean Engineering and Science 2021年第1期6卷 30-39页

作者： Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial UniversityLucknow-Deva RoadUttar Pradesh-225003India Department of Applied Science and Humanities Government Engineering CollegeNawadaDepartment of Science and TechnologyBihar-805122India Department of Mathematics JECRC UniversityJaipur-303905RajasthanIndia Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

关键词： Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform

Network and plage indices from Kodaikanal Ca-K data

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Research in Astronomy and Astrophysics 2014年第2期14卷 229-232页

作者： K.P.Raju Jagdev Singh Indian Institute of Astrophysics

The Ca II K filtergrams from Kodaikanal Solar Observatory have been used to study solar activity. The images are dominated by the chromospheric network and plages. Programs have been developed to obtain the network and plage indices from the daily images as functions of solar latitude and time. Preliminary results from the analysis are reported here. The network and plage indices were found to follow the sunspot cycle. A secondary peak is found during the period of declining activity in both the indices. A comparison of network indices from the northern and the southern hemispheres shows that the former is more active than the latter. However such an asymmetry is not clearly seen in the plage index.

关键词： Sun chromosphere

An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma

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Journal of Ocean Engineering and Science 2019年第2期4卷 85-99页

作者： Amit Goswami Jagdev Singh Devendra Kumar Sumit Gupta Sushila Department of Physics Jagan Nath UniversityJaipur 303901RajasthanIndia Department of Mathematics JECRC UniversityJaipur 303905RajasthanIndia Department of Mathematics University of RajasthanJaipur 302004RajasthanIndia Department of Mathematics Swami Keshvanand Institute of TechnologyManagement and GramothanRamnagariaJaipur 302017RajasthanIndia Department of Physics Vivekananda Global UniversityJaipur 303012RajasthanIndia

In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.

关键词： Sumudu transform scheme Homotopy perturbation technique RLW equations Ion acoustic wave Shallow water waves in oceans.

Numerical study of fractional model of multi-dimensional dispersive partial differential equation

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Journal of Ocean Engineering and Science 2019年第4期4卷 338-351页

作者： Vijay Verma Amit Prakash Devendra Kumar Jagdev Singh Department of Mathematics Pt.C.L.S.Govt.(PG)CollegeKarnalHaryanaIndia Department of Mathematics National Institute of TechnologyKurukshetra 136119India Department of Mathematics University of RajasthanJaipur 302004RajasthanIndia Department of Mathematics JECRC UniversityJaipur 303905RajasthanIndia

This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.

关键词： Homotopy perturbation method Fractional trigonometric function He’s polynomials Adomian decomposition method Sumudu transform

Variation of Small Scale Magnetic Fields Over a Century using Ca-K Images as Proxy

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Research in Astronomy and Astrophysics 2023年第4期23卷 172-183页

作者： Jagdev Singh Muthu Priyal B.Ravindra Luca Bertello Alexei Pevtsov Indian Institute of Astrophysics II BlockKoramangalaBengaluru–560034India National Solar Observatory 3365 Discovery DriveThird FloorBoulderCO 80303USA

A combined uniform and long-time series of Ca-K images from the Kodaikanal Observatory,Mount Wilson Observatory and Mauna Loa Solar Observatory was used to identify and study the Ca-K small-scale features and their solar cycle variations over a century.The small scale features are classified into three distinct categories:enhanced network,active network and quiet network.All these features show that their areas vary according to the11 yr solar cycle.The relative amplitude of the Ca-K network variations agrees with that of the sunspot cycle.The total area of these small-scale features varies from about 5%during the minimum phase of the solar cycle to about20%during its maximum phase.

关键词： Sun activity-Sun chromosphere-(Sun:)sunspots

Fractal dynamics and computational analysis of local fractional Poisson equations arising in electrostatics

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Communications in Theoretical Physics 2023年第12期75卷 12-18页

作者： Jagdev Singh Hassan Kamil Jassim Devendra Kumar Ved Prakash Dubey Department of Mathematics JECRC UniversityJaipurRajasthanIndia Department of Mathematics Kyung Hee University26 Kyungheedae-roDongdaemun-guSeoul02447Republic of Korea Department of Computer Science and Mathematics Lebanese American UniversityBeirutLebanon Department of Mathematics Faculty of Education for Pure SciencesUniversity of Thi-QarNasiriyahIraq Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial UniversityBarabanki-225003Uttar PradeshIndia

In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution.Numerical examples with computer simulations are presented in this paper.The obtained results show that LFNDM is effective and convenient for application.

关键词： poisson equation local fractional natural transform adomian decomposition method local fractional derivative electrostatics fractal media

Determination of the chromospheric quiet network element area index and its variation between 2008 and 2011

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Research in Astronomy and Astrophysics 2012年第2期12卷 201-211页

作者： Jagdev Singh Ravindra Belur Selvendran Raju Kumaravel Pichaimani Muthu Priyal Thambaje Gopalan Priya Amareswari Kotikalapudi Indian Institute of Astrophysics Koramangala

In general, it is believed that plages and sunspots are the main contribu- tors to solar irradiance. There are small-scale structures on the Sun with intermediate magnetic fields that could also contribute to solar irradiance, but it has not yet been quantified how many of these small scale structures contribute and how much this varies over the solar cycle. We used Ca II K images obtained from the telescope at the Kodaikanal observatory. We report a method to separate the network elements from the background structure and plage regions, and compute the changes in the network element area index during the minimum phase of the solar cycle and part of the as- cending phase of cycle 24. The measured area occupied by the network elements is about 30% and the plages cover less than 1% of the solar disk during the observation period from February 2008 to 2011. During the extended period of minimum activity, it is observed that the network element area index decreases by about 7% compared to the area occupied by the network elements in 2008. A long term study of the network element area index is required to understand the variations over the solar cycle.

关键词： Sun： network - Sun： Ca-K - Sun： solar cycle

Plant Community and Nutrient Status of the Soils of Schirmacher Oasis,East Antarctica

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Chinese Journal of Polar Science 2008年第1期19卷 63-76页

作者： Shiv Mohan singh jagdev Sharma Rasik Ravindra Purnima singh National Centre for Antarctic and Ocean research National Research Centre for grapes Purvanchal University Jaunpur India

Investigations on plant community and micronutrient status of Schirmacher Oasis, East Antarctica have been presented in this paper. The dominant plant communities include moss and lichen. The frequency of species occurrence and changes in species composition at different location varied. Thirty-four soil samples were ana- lyzed for chemical properties of the soils of Schirmacher Oasis and Nunatak, East Antarctica. The most common plant species growing throughout the areas of Sehirmacher Oasis and Nunataks are： Candelariella tiara （ lichen ） and Bryum pseudotriquetrum （moss）. Large variations were observed among different soil samples in all the nutri- ents and other measured soil chemical parameters. The soils are characterized by a-cidic pH ranging from 4.42 - 6.80. The mean organic carbon content was 0.62 and ranged from 0. 06 - 1.29%. The electrical conductivity in 1 ： 2 soil water ratio ranged from 0.06 - 1.29. The average content of macronutrient cation, which are ammonium acetate extractable was in the order of Ca 〉 K 〉 Na 〉 Mg. The average content of DTPA extractable micronutrient cations was in the order of Fe 〉 Mn 〉 Cu 〉 Zn. Thirty one out of 34 samples contained less than 0.80 ppm DTPA extractable Zn. Correlation studies revealed that content of macronutrient cations significantly and positively correlated to that of chlorides. Electrical conductivity exhibited significant and positive relationship with pH, K, Ca, Mg, Na and chloride content. Sodium （r =0.876 ＊＊） exhibited highest correlation followed by K （r =0. 831 ＊＊） with chlo- ride content. The correlation coefficient for chlorides was higher with electrical conductivity （r=0.732＊＊） than pH （r =0. 513 ＊＊）. Organic carbon content of the soil was positively correlated with Fe （ r = 0. 442 ＊）. The nutrient status did not appear to be a limiting factor in growth of plants. Lichen and moss community structure and composition in the study area were not related with fertility status of soil. Terrestrial mosses are most abundant and luxuriant alo

关键词： Antarctica Schirmacher Oasis Nutrient Lichen Moss.

Full-disk synoptic observations of the chromosphere using Hα telescope at the Kodaikanal Observatory

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Research in Astronomy and Astrophysics 2016年第8期16卷 79-88页

作者： Belur Ravindra Kesavan Prabhu Komandur Elayaveilli Rangarajan Bagare Shekar singh jagdev Kemkar Madan Mohan Paul Lancelot Koyipurathu Chellappan Thulasidharen Francis Gabriel Raju Selvendran Indian Institute of Astrophysics Ilnd BlockKoramangalaBengaluru-560034India

This paper reports on the installation and observations of a new solar telescope installed on 2014 October 7 at the Kodaikanal Observatory. The telescope is a refractive type equipped with a tunable Lyot Hα filter. A CCD camera with size 2k ×2k acquires images of the Sun and has a pixel size of 1.21″ pixel^-1 and a full field-of-view of 41＇. The telescope is equipped with a guiding system which keeps the image of the Sun within a few pixels throughout the observations. The FWHM of the Lyot filter is 0.4A and the filter is motorized, capable of scanning the Hα line profile at a smaller step size of 0.01 A. Partial-disk imaging covering about 10＇ is also possible with the help of a relay lens kept in front of the CCD camera. In this paper, we report the detailed specifications of the telescope, filter unit, the installation, observations and the procedures we have followed to calibrate and align the data. We also present preliminary results with this new full-disk telescope.

关键词： Sun： chromosphere-- instrumentation miscellaneous -- telescopes solar telescope -- objectSun -- observations Hα